Math CentralQuandaries & Queries


Question from Robert, a student:

What is the domain of the function (3x+4)/x^2+5x+6

Hi Robert,

Think of a function as a process or a recipe. You input a value, the value of x, some calculation goes on in the background and the function returns a numeric value. For example if you input x = 2 to the function you sent


the value returned is 1/2. For some input values however a function might not work. If the function is √x (the √ button on your calculator) and you input x = -2 then the function doesn't return a value. (My calculator says Not a number.) Likewise if the function is 3/x and you input x = 0 then the function doesn't return a number. (When I try to divide 3 by 0 my calculator says Infinity which is not a number.)

The domain of a function is all inputs x that return a numeric value. For the function √x if x is positive r zero then a numeric value is returned but if x is negative then the function fails. Thus the doa min of √x is all x greater than or equal to zero.

For the function 3/x every value of x except x = 0 returns a numeric value so the domain of 3/x is all real numbers x except x = 0.

For your function


Every value of x will return a number except x values that yield a zero in the denominator. What values of x make x2 + 5x + 6 = 0?


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